Related papers: Direct coupling of continuum and shell elements in…
Shells, i.e., objects made of a thin layer of material following a surface, are among the most common structures in use. They are highly efficient, in terms of material required to maintain strength, but also prone to deformation and…
For the finite element simulation of thin soft biological tissues in dynamics, shell elements, compared to volume elements, can capture the whole tissue thickness at once, and feature larger critical time steps. However, the capabilities of…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…
We propose and explore a new, general-purpose method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn its finite element discretization leads to an efficient alternating…
Contact involving soft materials often combines dry adhesion, sliding friction, and large deformations. At the local level, these three aspects are rarely captured simultaneously, but included in the theoretical models by Mergel et al.…
In this paper, we present a 2D numerical model developed to simulate the dynamics of soft, deformable particles. To accommodate significant particle deformations, the particle surface is represented as a narrow shell composed of mass points…
Hard-magnetic soft materials (HMSMs) are particulate composites that consist of a soft matrix embedded with particles of high remnant magnetic induction. Since the application of an external magnetic flux induces a body couple in HMSMs, the…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation.…
In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is shown how to transform the stored elastic energy for an…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…
One of the main approaches for modeling fracture and crack propagation in solid materials is adaptive insertion of cohesive elements, in which line-like (2D) or surface-like (3D) elements are inserted into the finite element mesh to model…